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<b>let </b><font color="Maroon" title="c1">T</font> be   <a href="topgrp_1.html#NM4" title="TOPGRP_1:NM.4">TopGroup</a>;<br/>

<b>assume </b><a NAME="E1:86_1_1"/>
<font color="Maroon" title="c1">T</font> is <a href="topgrp_1.html#V4" title="TOPGRP_1:attr.4">BinContinuous</a>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c2">G</font> = <font color="Maroon" title="c1">T</font> as  <a href="topgrp_1.html#V4" title="TOPGRP_1:attr.4">BinContinuous</a> <a href="topgrp_1.html#NM4" title="TOPGRP_1:NM.4">TopGroup</a> ;<br/>
<a NAME="E3:86_1_1"/>
<font color="Maroon" title="c2">G</font> is <a href="topgrp_1.html#V1" title="TOPGRP_1:attr.1">homogeneous</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="86_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">p</font>, <font color="Maroon" title="c4">q</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">G</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="topgrp_1.html#D6" target="_self" title="TOPGRP_1:def.6">TOPGRP_1:def 6</a><br/>

<b>take </b>
 <a href="topgrp_1.html#K8" title="TOPGRP_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a> </span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">q</font></span>)</span>
;<br/>

<b>thus </b><span class="p1">(<span class="default"><a href="topgrp_1.html#K8" title="TOPGRP_1:func.8">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a> </span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">q</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">p</font> = 
<font color="Maroon" title="c3">p</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a> </span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">q</font></span>)</span>
<b>by </b><i><a class="ref" href="topgrp_1.html#D2" target="_self" title="TOPGRP_1:def.2">Def2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a> </span>)</span></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">q</font>
<b>by </b><i><a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c2">G</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">q</font>
<b>by </b><i><a class="ref" href="group_1.html#D6" title="GROUP_1:def.6">GROUP_1:def 6</a></i>
<br/>.= 
<font color="Maroon" title="c4">q</font>
<b>by </b><i><a class="ref" href="group_1.html#D5" title="GROUP_1:def.5">GROUP_1:def 5</a></i>
;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:86_1_1"/>
<font color="Maroon" title="c1">T</font> is <a href="topgrp_1.html#V1" title="TOPGRP_1:attr.1">homogeneous</a>
 ;<br/>


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